I'm having some trouble with the following problems.

Use a linear approximation (or differentials) to estimate the given number.

- (8.06)^(2/3)
- 1/1002

My book doesn't go over the process of how to do these problems. Thanks for any help.

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- Oct 26th 2008, 07:36 AMdm10Estimate the Given Number
I'm having some trouble with the following problems.

Use a linear approximation (or differentials) to estimate the given number.

- (8.06)^(2/3)
- 1/1002

My book doesn't go over the process of how to do these problems. Thanks for any help. - Oct 26th 2008, 08:04 AMThePerfectHacker
Let $\displaystyle f(x) = (8+x)^{2/3}$ then $\displaystyle f(h) \approx f(0) + hf'(0)$

Now $\displaystyle f'(x) = \tfrac{2}{3}(8+x)^{-1/3} \implies f'(0) = \tfrac{2}{3}\cdot 8^{-1/3} = \tfrac{1}{3}$

This means, $\displaystyle f(h) \approx 2 + \tfrac{h}{3}$

Now let $\displaystyle h=.06$

The other problem is similar.